Question

A particle moves along the x-axis obeying the equation $x=t(t-1)(t-2)$, where $x$ is in meter and $t$ is in second
Find the time when the displacement of the particle is zero.

Answer 1

$x=t[t-1][t-2]=(t^2-t)(t-2)$

$=t^3-2t^2-t^2+2t=t^3-3t^2+2t$

$v=\frac{dx}{dt}=3t^2-6t+2$

$x=0\Rightarrow t=0s,t=1s,t=2s$